Controlled differential equations as rough integrals
Hoang Duc Luu
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Submission date: 13. Jul. 2020 (revised version: October 2020)
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We study controlled diﬀerential equations with unbounded drift terms, where the driving paths is ν - Hölder continuous for ν ∈ (,), so that the rough integral are interpreted in the Gubinelli sense for controlled rough paths. Similar to the rough diﬀerential equations in the sense of Lyons or of Friz-Victoir, we prove the existence and uniqueness theorem for the solution in the sense of Gubinelli, the continuity on the initial value, and the solution norm estimates.